Exponential decay of a thermoelastic system for a thin plate under periodic sunlight (Q1748315)

The authors study the asymptotic properties of a thermoelastic plate model subject to different sets of boundary conditions, such as Dirichlet, Neumann or natural. The latter correspond to a thermal insulated boundary with clamped edge. They show that the pair composed of the Laplacian of the vertical deflection from the ``middle surface'' of a thin plate and the vertical temperature gradient of the thin plate converges to the equilibrium state exponentially fast. For the natural boundary conditions, the authors focus on the one-dimensional setting and solve an eigenvalue problem.